Limits MCQs

श्रेणी: Mathematics | विषय: Advanced Mathematics | टॉपिक: Limits

3 प्रश्न सेव किए MCQs Saved MCQs

Advanced Mathematics • Limits

Calculate lim (x^2 - 4)/(x^2 + 5x - 14) as x approaches 2. Calculate lim (x^2 - 4)/(x^2 + 5x - 14) as x approaches 2.

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A. Undefined Undefined B. 2/7 2/7 C. 4/5 4/5 D. 4/9 4/9

सही उत्तर: D Correct Answer: D

Factor and cancel x - 2: (x^2 - 4)/(x^2 + 5x - 14) = (x + 2)/(x + 7). At x = 2 this equals 4/9.

Advanced Mathematics • Limits

In which one of the following cases does the limit exist? In which one of the following cases does the limit exist?

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A. lim as (x,y,z)->(0,0,0) of (x^2 + 2y^2 + 3z^2)/(x^2 + y^2 + z^2) lim as (x,y,z)->(0,0,0) of (x^2 + 2y^2 + 3z^2)/(x^2 + y^2 + z^2) B. lim as (x,y)->(0,0) of (2x^2 + sin^2(y))/(x^2 + y^2) lim as (x,y)->(0,0) of (2x^2 + sin^2(y))/(x^2 + y^2) C. lim as (x,y)->(0,0) of 5x^2y/(x^2 + y^2) lim as (x,y)->(0,0) of 5x^2y/(x^2 + y^2) D. lim as (x,y,z)->(0,0,0) of (2x^2 + 2y^2 - z^2)/(x^2 + y^2 + z^2) lim as (x,y,z)->(0,0,0) of (2x^2 + 2y^2 - z^2)/(x^2 + y^2 + z^2)

सही उत्तर: C Correct Answer: C

For option C, |5x^2y/(x^2+y^2)| <= 5|y|, which tends to zero. The other expressions have different limits along different coordinate directions.

Advanced Mathematics • Limits

Evaluate lim as (x,y,z) approaches (3,0,1) of exp(-x)y sin(xy/z). Evaluate lim as (x,y,z) approaches (3,0,1) of exp(-x)y sin(xy/z).

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A. pi pi B. 1 1 C. 0 0 D. Does not exist Does not exist

सही उत्तर: C Correct Answer: C

The function is continuous at (3,0,1), since z is nonzero there. Direct substitution gives e^(-3) x 0 x sin(0)=0.

Limits MCQs

Limits MCQs

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